GRADING AND SCREENING 225
At regular intervals in the expansion chamber gates must be placed to receive the gradings which will be more or less of a size inversely proportional to the mean cross-sectional area of the grading chamber within the draw-off radius of the gates. These gates are usually held to place by a lever and weight. When sufficient material has collected above the gate more than to counterbalance it, the gate opens and permits the grading to discharge. Gates of this kind are necessary to prevent the air from passing through the discharge passages, taking with it material which does not belong at these points.
Expansion chambers can be placed horizontally, on an inclination or vertically. The inclined chambers lend themselves to the simplest means for discharging the gradings as it is only necessary to suspend from the expansion chamber a series of hoppers with discharge means at the bottom, these hoppers will increase in dimensions from the entry to the discharge end. The inclined and vertical expansion chambers have the disadvantage that they take up more head room, than horizontal ones. For vertical expansion chambers the simplest arrangement is a series of double cones or pyramids of increasing size, the pairs being placed in a vertical line, the smallest one being at the entry and the largest at the top. The gradings are caught within the inner cone and the air current circulates between the inner and outer cones. With the vertical forms the air has the power to balance a grain of a particular size or weight, the balance being dependent upon the velocity, and this in turn upon the initial velocity created by the fan, and the area of the cross-section at the point of balance.
Air grading is little practiced today. At one time it was a standard method for •preparing sandpaper gradings. It requires large and costly settlement chambers. It is impossible to prevent eddying currents due to variations in the blast and fric-tional contact with the sides of the expansion chamber. It would be possible to produce uniformity in the velocity of the air currents by the use of gratings as is done in the air tunnels for aviation experimental work did not such gratings interfere with settlement.
Dust will cling to the walls of the grading chamber until the collection is so heavy it falls off in mass. These dust falls seriously contaminate the gradings. It is very difficult to feed the granulated mass evenly to the blower. The most satisfactory feeding devices are those which mechanically put the grains in motion in the same direction as the air blast and with the same velocity.
Theory of Blowing.—There is very little theory to this type of apparatus. For upward currents the balancing current from point to point can be deduced. It is of course equal to the velocity of fall the particle attains under gravity. In the inclined forms of chamber the pressure of the air current is balanced against the inclined component of gravity.1
1 For particles whose fall velocity is very small owing to minute size the formula of Stokes corrected by experiment will apply. In this formula the resistance is assumed to vary directly as the velocity. Professor R. A. Millikan has long been an experimental investigator of the fall velocity of small particles falling through various media and gives as the result of his latest experimental work:
A' = .864 + .29c ' € g = the constant of gravity <r = the density of air P = the density of the falling droplet e = the Naperian base (2.7182818) a = the radius of droplet. I = the mean free path derived from
77 = .3502dc/ and c = \/^~ A/^